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Exam 2: An Introduction to Linear Programming

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Question 1

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Use this graph to answer the questions. ​ a.Which area (I,II,III,IV,or V)forms the feasible region? b.Which point (A,B,C,D,or E)is optimal? c.Which constraints are binding? d.Which slack variables equal zero? ​

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a. Area III is the feasible re...

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Question 2

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Solve the following system of simultaneous equations.6X + 4Y = 40 2X + 3Y = 20

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Maxwell Manufacturing makes two models of felt-tip marking pens.Requirements for each lot of pens are given below. ​ The profit for either model is $1000 per lot. a.What is the linear programming model for this problem? b.Find the optimal solution. c.Will there be excess capacity in any resource? ​

All linear programming problems have all of the following properties EXCEPT

Muir Manufacturing produces two popular grades of commercial carpeting among its many other products.In the coming production period,Muir needs to decide how many rolls of each grade should be produced in order to maximize profit.Each roll of Grade X carpet uses 50 units of synthetic fiber,requires 25 hours of production time,and needs 20 units of foam backing.Each roll of Grade Y carpet uses 40 units of synthetic fiber,requires 28 hours of production time,and needs 15 units of foam backing.​ The profit per roll of Grade X carpet is $200,and the profit per roll of Grade Y carpet is $160.In the coming production period,Muir has 3000 units of synthetic fiber available for use.Workers have been scheduled to provide at least 1800 hours of production time (overtime is a possibility).The company has 1500 units of foam backing available for use.​ Develop and solve a linear programming model for this problem.

In a linear programming problem,the objective function and the constraints must be linear functions of the decision variables.

For a minimization problem,the solution is considered to be unbounded if the value may be made infinitely small.

The three assumptions necessary for a linear programming model to be appropriate include all of the following EXCEPT

A variable added to the left-hand side of a less-than-or-equal-to constraint to convert the constraint into an equality is a

The constraint 2x₁ − x₂ = 0 passes through the point (200,100).

The point (3,2)is feasible for the constraint 2x₁ + 6x₂ ≤ 30.

Does the following linear programming problem exhibit infeasibility,unboundedness,or alternative optimal solutions? Explain.

For the following linear programming problem,determine the optimal solution using the graphical solution method.Are any of the constraints redundant? If yes,identify the constraint that is redundant.

When no solution to the linear programming problem satisfies all the constraints,including the nonnegativity conditions,it is considered

A redundant constraint results in

Constraints limit the degree to which the objective in a linear programming problem is satisfied.

Which of the following special cases does NOT require reformulation of the problem in order to obtain a solution?

A linear programming problem can be both unbounded and infeasible.

Consider the following linear programming problem: ​ a.Use a graph to show each constraint and the feasible region. b.Identify the optimal solution point on your graph.What are the values of X and Y at the optimal solution? c.What is the optimal value of the objective function?

Only binding constraints form the shape (boundaries)of the feasible region.